A scalar is a quantity that has only a size (magnitude) and no direction. Distance, speed, mass and time are all scalar quantities.

A vector is a quantity that has both a size (magnitude) and a direction . Displacement, velocity, acceleration and force are all vector quantities.

True or False? A speed can be negative if an object is moving backwards.

False. Speed is a scalar , so it has a size but no direction, and it cannot be negative. It is the velocity that is negative when an object moves in the direction chosen as negative. Its speed is the size of that velocity.

Define fundamental units .

Fundamental units , also called S.I. units , are the internationally agreed standard units of measurement. The three needed in mechanics are the metre (m) for length, the second (s) for time and the kilogram (kg) for mass. Every other unit in mechanics is built from these.

A force is a push or a pull acting on an object. A force is a vector , so it has both a size and a direction, and it is measured in newtons (N) .

A piece of equipment is taken from the Earth to the Moon. Which of its mass and its weight changes, and why?

The weight changes and the mass does not. Mass measures the amount of matter in an object, which is the same wherever the object is. Weight is mass multiplied by the acceleration due to gravity, and that acceleration is different on the Moon.

True or False? The normal reaction from a surface always acts vertically upwards.

False. A normal reaction always acts perpendicular to the surface producing it. That is vertically upwards only when the surface is horizontal. On a slope the reaction is perpendicular to the slope, so it is not vertical.

In which direction does a frictional force act on an object resting on, or sliding along, a surface?

Friction acts along the surface , in the direction opposite to the way the object is moving, or would move if there were no friction. Friction is a resistive force, so it opposes the movement of the object relative to the surface.

Why are simplifying assumptions made when a real life situation is turned into a mechanics problem?

Real situations are too complicated to describe exactly. Assumptions strip out the features that matter least, so that the situation can be described by equations or graphs that can actually be solved.

Define particle , as the word is used in modelling.

A particle is an object whose dimensions are treated as negligible , so that it occupies a single point. Every force acting on it can then be taken to act at that same point, and effects that depend on its size or shape, such as spin, are ignored.

A string is modelled as light . What does that mean, and what does it let you assume about the tension in the string?

A light string is one with zero mass . Its weight can then be ignored, so the tension is the same all the way along the string, and the same at each end.

Two objects are connected by a string that is modelled as inextensible . What does that let you assume about their motion?

An inextensible string cannot stretch , so the distance between the two objects cannot change. The two objects therefore move with the same speed and the same acceleration .

Define uniform , as the word is used to describe an object in a model.

A uniform object is one whose mass is spread evenly through it. Its weight can then be taken to act at a single point at the centre of the object.

A pulley is modelled as smooth . What does that let you assume about the string passing over it?

A smooth pulley exerts no friction on the string. The tension is therefore the same on both sides of the pulley.

True or False? Air resistance should be included in a mechanics model unless a question tells you to ignore it.

False. Air resistance is normally assumed to be negligible , and is left out unless a question says otherwise. It is one of the standard simplifying assumptions, and putting it back in is one way of making a model more realistic.

The answer produced by a mathematical model does not seem reasonable. What should be done next?

The assumptions behind the model should be reconsidered and criticised, and the model refined. The refined model is then solved again and its answer checked for reasonableness, and that cycle repeats until the answer is acceptable.

A ball thrown through the air is modelled as a particle moving with no air resistance. Suggest two ways of making the model more realistic.

Two possible refinements are to include air resistance and to allow for the size and shape of the ball instead of treating it as a particle. Others include allowing for the spin of the ball, allowing for the wind, and using a more accurate value for the acceleration due to gravity.

A LevelMathsEdexcelMechanicsFlashcardsQuantities & Units in MechanicsQuantities, Units & Modelling

Quantities, Units & Modelling (Edexcel A Level Maths: Mechanics): Flashcards

Exam code: 9MA0

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Cards in this collection (34)

Define scalar.
A scalar is a quantity that has only a size (magnitude) and no direction.
Distance, speed, mass and time are all scalar quantities.
Two cars are travelling along a straight road, with one having a velocity of $7 {m s}^{- 1}$ and the other having a velocity of $- 7 {m s}^{- 1}$ . What does the difference in sign tell you about their motion?
The two cars are travelling at the same speed but in opposite directions.
Velocity is a vector, so the sign records the direction of travel. Which direction counts as positive is a choice made at the start of a problem.
Define vector.
A vector is a quantity that has both a size (magnitude) and a direction.
Displacement, velocity, acceleration and force are all vector quantities.
True or False?
A speed can be negative if an object is moving backwards.
False.
Speed is a scalar, so it has a size but no direction, and it cannot be negative.
It is the velocity that is negative when an object moves in the direction chosen as negative. Its speed is the size of that velocity.
Complete the definitions of these two vector quantities:
Displacement is the $______$ moved in a given direction from a starting point.
Velocity is the $______$ of an object in a given direction.
Displacement is the distance moved in a given direction from a starting point.
Velocity is the speed of an object in a given direction.
How are vector quantities written in printed material such as textbooks and exam papers, and how should you write them by hand?
In print a vector is written in bold, upright type, for example $F$ .
Bold cannot be reproduced in handwriting, so by hand a vector is underlined instead.
Define fundamental units.
Fundamental units, also called S.I. units, are the internationally agreed standard units of measurement.
The three needed in mechanics are the metre (m) for length, the second (s) for time and the kilogram (kg) for mass.
Every other unit in mechanics is built from these.
Complete the conversions between units of length and of mass:
$1 km =______m$
$1 m =______cm$
$1 kg =______g$
The completed conversions are:
$1 km = 1000 m$
$1 m = 100 cm$
$1 kg = 1000 g$
Lengths must be converted into metres and masses into kilograms before they are used in a calculation.
A time is given as 17 minutes and 42 seconds. Convert it into S.I. units.
The time is 1062 seconds.
Each minute is 60 seconds, so $17 \times 60 = 1020$ seconds, and $1020 + 42 = 1062$ seconds.
True or False?
To convert a time given in hours into seconds, you multiply by 60.
False.
Multiplying by 60 converts hours into minutes. Hours are converted into seconds by multiplying by 60 twice, which is multiplying by 3600.
For example, $3.8$ hours is $3.8 \times 3600 = 13680$ seconds.
Convert $0.054$ grams into kilograms, giving your answer in standard form.
The mass is $5.4 \times 10^{- 5} kg$ .
There are 1000 grams in a kilogram, so grams are divided by 1000: $0.054 \div 1000 = 0.000054$ .
Define derived unit.
A derived unit is a unit built by combining the fundamental units of length, time and mass.
For example, a velocity is a distance divided by a time, so it is measured in ${m s}^{- 1}$ .
Convert a speed of $5.8 {km h}^{- 1}$ into ${m s}^{- 1}$ , giving your answer to 3 significant figures.
The speed is $1.61 {m s}^{- 1}$ .
There are 1000 metres in a kilometre and 3600 seconds in an hour, so $5.8 \times 1000 \div 3600 = 1.611 \dots$
Fill in the missing S.I. units:
Velocity is measured in $______$ , acceleration is measured in $______$ , and force is measured in $______$ .
Velocity is measured in ${m s}^{- 1}$ , acceleration is measured in ${m s}^{- 2}$ , and force is measured in newtons (N), which is the same as ${kg m s}^{- 2}$ .
When converting an acceleration from ${km h}^{- 2}$ into ${m s}^{- 2}$ , why do you divide by $3600^{2}$ rather than by $3600$ ?
The unit of time is squared in ${km h}^{- 2}$ , so the conversion factor for time has to be squared as well.
One hour is 3600 seconds, so $1 {km h}^{- 2} = 1000 \div 3600^{2} {m s}^{- 2}$ .
True or False?
Speed and velocity are measured in the same units.
True.
Speed and velocity are both measured in ${m s}^{- 1}$ .
A velocity is a speed together with a direction, and adding a direction does not change the unit.
For a density is given as $14 {g cm}^{- 3}$ , converting it into ${kg m}^{- 3}$ means dividing by 1000 for the mass, but multiplying by $100^{3}$ for the volume. Why multiply?
In ${g cm}^{- 3}$ the centimetres are in the denominator, so that part of the conversion works the opposite way round.
One metre is 100 cm, so one cubic metre holds $100^{3}$ cubic centimetres, and a quantity given per cubic centimetre is $100^{3}$ times as much per cubic metre.
Here $14 \div 1000 \times 100^{3} = 14000 {kg m}^{- 3}$ .
Speed is measured in ${m s}^{- 1}$ . What does that unit tell you about the formula for speed?
The unit ${m s}^{- 1}$ means metres divided by seconds, which is a distance divided by a time, so
$speed = \frac{distance}{time}$
A forgotten formula can often be rebuilt this way, from the units the quantity is measured in.
Define force.
A force is a push or a pull acting on an object.
A force is a vector, so it has both a size and a direction, and it is measured in newtons (N).
Fill in the missing directions:
A tension is a pulling force, which acts $______$ from an object.
A thrust is a pushing force, which acts $______$ an object.
A tension is a pulling force, which acts away from an object.
A thrust is a pushing force, which acts towards an object.
Define weight.
The weight of an object is the force on it due to gravity.
An object of mass $m$ kilograms has weight $W = m g$ newtons, where $g$ is the acceleration due to gravity.
Weight always acts vertically downwards.
A piece of equipment is taken from the Earth to the Moon. Which of its mass and its weight changes, and why?
The weight changes and the mass does not.
Mass measures the amount of matter in an object, which is the same wherever the object is. Weight is mass multiplied by the acceleration due to gravity, and that acceleration is different on the Moon.
True or False?
The normal reaction from a surface always acts vertically upwards.
False.
A normal reaction always acts perpendicular to the surface producing it.
That is vertically upwards only when the surface is horizontal. On a slope the reaction is perpendicular to the slope, so it is not vertical.
In which direction does a frictional force act on an object resting on, or sliding along, a surface?
Friction acts along the surface, in the direction opposite to the way the object is moving, or would move if there were no friction.
Friction is a resistive force, so it opposes the movement of the object relative to the surface.
Why are simplifying assumptions made when a real life situation is turned into a mechanics problem?
Real situations are too complicated to describe exactly.
Assumptions strip out the features that matter least, so that the situation can be described by equations or graphs that can actually be solved.
Define particle, as the word is used in modelling.
A particle is an object whose dimensions are treated as negligible, so that it occupies a single point.
Every force acting on it can then be taken to act at that same point, and effects that depend on its size or shape, such as spin, are ignored.
A string is modelled as light. What does that mean, and what does it let you assume about the tension in the string?
A light string is one with zero mass.
Its weight can then be ignored, so the tension is the same all the way along the string, and the same at each end.
Fill in the two words used to describe surfaces in a model:
A $______$ surface has no friction.
A $______$ surface exerts a frictional force on an object in contact with it.
A smooth surface has no friction.
A rough surface exerts a frictional force on an object in contact with it.
Two objects are connected by a string that is modelled as inextensible. What does that let you assume about their motion?
An inextensible string cannot stretch, so the distance between the two objects cannot change.
The two objects therefore move with the same speed and the same acceleration.
Define uniform, as the word is used to describe an object in a model.
A uniform object is one whose mass is spread evenly through it.
Its weight can then be taken to act at a single point at the centre of the object.
A pulley is modelled as smooth. What does that let you assume about the string passing over it?
A smooth pulley exerts no friction on the string.
The tension is therefore the same on both sides of the pulley.
True or False?
Air resistance should be included in a mechanics model unless a question tells you to ignore it.
False.
Air resistance is normally assumed to be negligible, and is left out unless a question says otherwise.
It is one of the standard simplifying assumptions, and putting it back in is one way of making a model more realistic.
The answer produced by a mathematical model does not seem reasonable. What should be done next?
The assumptions behind the model should be reconsidered and criticised, and the model refined.
The refined model is then solved again and its answer checked for reasonableness, and that cycle repeats until the answer is acceptable.
A ball thrown through the air is modelled as a particle moving with no air resistance. Suggest two ways of making the model more realistic.
Two possible refinements are to include air resistance and to allow for the size and shape of the ball instead of treating it as a particle.
Others include allowing for the spin of the ball, allowing for the wind, and using a more accurate value for the acceleration due to gravity.

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